The adiabatic control is a powerful technique for many practical applications in quantum state engineering,light-driven chemical reactions and geometrical quantum computations.This paper reveals a speed limit of nonad...The adiabatic control is a powerful technique for many practical applications in quantum state engineering,light-driven chemical reactions and geometrical quantum computations.This paper reveals a speed limit of nonadiabatic transition in a general time-dependent parametric quantum system that leads to an upper bound function which lays down an optimal criteria for the adiabatic controls.The upper bound function of transition rate between instantaneous eigenstates of a time-dependent system is determined by the power fluctuations of the system relative to the minimum gap between the instantaneous levels.In a parametric Hilbert space,the driving power corresponds to the quantum work done by the parametric force multiplying the parametric velocity along the parametric driving path.The general two-state time-dependent models are investigated as examples to calculate the bound functions in some general driving schemes with one and two driving parameters.The calculations show that the upper bound function provides a tighter real-time estimation of nonadiabatic transition and is closely dependent on the driving frequencies and the energy gap of the system.The deviations of the real phase from Berry phase on different closed paths are induced by the nonadiabatic transitions and can be efficiently controlled by the upper bound functions.When the upper bound is adiabatically controlled,the Berry phases of the electronic spin exhibit nonlinear step-like behaviors and it is closely related to topological structures of the complicated parametric paths on Bloch sphere.展开更多
In this paper, we investigate the third Hankel determinant H3(1) for the class Hσμ(λ,φ)(λ≥ 1,μ≥ 1) of Ma-Minda bi-univalent functions in the open unit disk D ={z :|z|<1} and obtain the upper bound of the ab...In this paper, we investigate the third Hankel determinant H3(1) for the class Hσμ(λ,φ)(λ≥ 1,μ≥ 1) of Ma-Minda bi-univalent functions in the open unit disk D ={z :|z|<1} and obtain the upper bound of the above determinant H3(1).展开更多
基金Project supported by the National Natural Science Foundation of China(Emergency Project,Grant Nos.11447025 and 11847308)
文摘The adiabatic control is a powerful technique for many practical applications in quantum state engineering,light-driven chemical reactions and geometrical quantum computations.This paper reveals a speed limit of nonadiabatic transition in a general time-dependent parametric quantum system that leads to an upper bound function which lays down an optimal criteria for the adiabatic controls.The upper bound function of transition rate between instantaneous eigenstates of a time-dependent system is determined by the power fluctuations of the system relative to the minimum gap between the instantaneous levels.In a parametric Hilbert space,the driving power corresponds to the quantum work done by the parametric force multiplying the parametric velocity along the parametric driving path.The general two-state time-dependent models are investigated as examples to calculate the bound functions in some general driving schemes with one and two driving parameters.The calculations show that the upper bound function provides a tighter real-time estimation of nonadiabatic transition and is closely dependent on the driving frequencies and the energy gap of the system.The deviations of the real phase from Berry phase on different closed paths are induced by the nonadiabatic transitions and can be efficiently controlled by the upper bound functions.When the upper bound is adiabatically controlled,the Berry phases of the electronic spin exhibit nonlinear step-like behaviors and it is closely related to topological structures of the complicated parametric paths on Bloch sphere.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11561001 11271045)+4 种基金the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(Grant No.NJYT-18-A14)the Natural Science Foundation of Inner Mongolia(Grant No.2018MS01026)the Higher School Foundation of Inner Mongolia(Grant Nos.NJZY17300 NJZY17301)the Natural Science Foundation of Chifeng of Inner Mongolia
文摘In this paper, we investigate the third Hankel determinant H3(1) for the class Hσμ(λ,φ)(λ≥ 1,μ≥ 1) of Ma-Minda bi-univalent functions in the open unit disk D ={z :|z|<1} and obtain the upper bound of the above determinant H3(1).
